| Title: | Implementation of the SVM-Maj Algorithm |
|---|---|
| Description: | Implements the SVM-Maj algorithm to train data with support vector machine <doi:10.1007/s11634-008-0020-9>. This algorithm uses two efficient updates, one for linear kernel and one for the nonlinear kernel. |
| Authors: | Hoksan Yip [aut, cre], Patrick J.F. Groenen [aut], Georgi Nalbantov [aut] |
| Maintainer: | Hoksan Yip <[email protected]> |
| License: | GPL-2 |
| Version: | 0.2.9.3 |
| Built: | 2024-11-23 17:15:29 UTC |
| Source: | CRAN |
Returns the area under the curve value as a fraction.
auc(q, y = attr(q, "y"))auc(q, y = attr(q, "y"))
q |
the predicted values |
y |
a list of the actual classes of |
the area under the curve value
df <- with(diabetes, cbind(y, X)) lm.y <- glm(y ~ ., data = df, family = binomial()) print(with(lm.y, auc(fitted.values, y)))df <- with(diabetes, cbind(y, X)) lm.y <- glm(y ~ ., data = df, family = binomial()) print(with(lm.y, auc(fitted.values, y)))
This file concerns credit card applications of 690 households.
This data set has been split into two components for the convenience of the model training.
data.frame-object X consists of with 6 numerical and 8
categorical attributes. The labels have been changed for the convenience of
the statistical algorithms. For example, attribute 4 originally had 3 labels
p,g,gg and these have been changed to labels 1,2,3.
Factor y indicates whether the application has been Accepted
or Rejected
The training set AusCredit.tr contains a randomly selected set of 400
subjects, and AusCredit.te contains the remaining 290 subjects.
AusCredit contains all 690 objects.
All attribute names and values have been changed to meaningless symbols to protect confidentiality of the data.
This dataset is interesting because there is a good mix of attributes – continuous, nominal with small numbers of values, and nominal with larger numbers of values. There are also a few missing values.
Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for support vector machines, 2001. Software available at https://www.csie.ntu.edu.tw/~cjlin/libsvm/.
attach(AusCredit) summary(X) summary(y) detach(AusCredit)attach(AusCredit) summary(X) summary(y) detach(AusCredit)
Given the predicted value q and the observed classes y,
it shows an overview of the prediction performances with hit rates,
misclassification rates, true positives (TP), false positives (FP)
and precision.
classification(q, y, classes = c("-1", "1"), weights = NULL)classification(q, y, classes = c("-1", "1"), weights = NULL)
q |
the predicted values |
y |
a list of the actual classes of |
classes |
a character vector with the labels of the two classes |
weights |
an optional parameter to specify a weighted hit rate and misclassification rate |
a list with three elements, matrix equals the confusion
matrix,overall equals the overall prediction performance and
in measures the measures per class is stored.
From National Institute of Diabetes and Digestive and Kidney Diseases.
X is a data frame of 768 female patients with 8 attributes.
no.pregnant |
number of pregnancies. |
glucose |
plasma glucose concentration in an oral glucose tolerance test |
blood.press |
diastolic blood pressure (mm Hg) |
triceps.thick |
triceps skin fold thickness (mm) |
insulin |
2-Hour serum insulin (mu U/ml) |
BMI |
body mass index (weight in kg/(height in m)**2) |
pedigree |
diabetes pedigree function |
age |
age in years |
y contains the class labels: Yes or No, for diabetic according
to WHO criteria.
The training set diabetes.tr contains a randomly selected set of 600
subjects, and diabetes.te contains the remaining 168 subjects.
diabetes contains all 768 objects.
Several constraints were placed on the selection of these instances from a larger database. In particular, all patients here are females at least 21 years old of Pima Indian heritage.
Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for support vector machines, 2001. Software available at https://www.csie.ntu.edu.tw/~cjlin/libsvm/.
Smith, J.W., Everhart, J.E., Dickson, W.C., Knowler, W.C., & Johannes, R.S. (1988). Using the ADAP learning algorithm to forecast the onset of diabetes mellitus. In Proceedings of the Symposium on Computer Applications and Medical Care (pp. 261–265). IEEE Computer Society Press.
attach(diabetes) summary(X) summary(y)attach(diabetes) summary(X) summary(y)
This function creates a function to compute the hinge error,
given its predicted value q and its class y,
according to the loss term of the Support Vector machine loss function.
getHinge(hinge = "quadratic", delta = 3, eps = 1e-08)getHinge(hinge = "quadratic", delta = 3, eps = 1e-08)
hinge |
Hinge error function to be used, possible values are
|
delta |
The parameter of the huber hinge
(only if |
eps |
Specifies the maximum steepness of the quadratic majorization
function |
The hinge error function with arguments q and y to
compute the hinge error. The function returns a list with the parameters
of the majorization function SVM-Maj (a, b and c)
and the loss error of each object (loss).
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
hingefunction <- getHinge() ## plot hinge function value and, if specified, ## the majorization function at z ## plot(hingefunction, z = 3) ## generate loss function value loss <- hingefunction(q = -10:10, y = 1)$loss print(loss) plot(hingefunction, z = 3)hingefunction <- getHinge() ## plot hinge function value and, if specified, ## the majorization function at z ## plot(hingefunction, z = 3) ## generate loss function value loss <- hingefunction(q = -10:10, y = 1)$loss print(loss) plot(hingefunction, z = 3)
Create a I-spline basis for an array. isb will equally distribute the
knots over the value range using quantiles.
isb(x, spline.knots = 0, knots = NULL, spline.degree = 1)isb(x, spline.knots = 0, knots = NULL, spline.degree = 1)
x |
The predictor variable, which will be transformed into I-spline basis. |
spline.knots |
Number of inner knots to use. |
knots |
An array consisting all knots (boundary knots as well as the interior knots) to be used to create the spline basis. |
spline.degree |
The polynomial degree of the spline basis. |
The I-spline with the used spline settings as attribute. The spline settings attribute can transform the same attribute of any other objects using the same knots.
Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
J.O. Ramsay (1988) Monotone regression splines in action. Statistical Science, 3(4):425-461
## plot the spline transformation given a monotone sequence B0 <- isb(0:100, spline.knots = 2, spline.degree = 3) plot(NULL, xlim = c(0, 140), ylim = c(0, 1), xlab = "x", ylab = "I-spline") for (i in 1:ncol(B0)) { lines(B0[, i], col = i, lwd = 3) } legend("bottomright", legend = 1:ncol(B0), col = 1:ncol(B0), lty = 1, lwd = 3, title = "Spline Columns" ) ## create I-spline basis for the first 50 observations x <- iris$Sepal.Length B1 <- isb(x[1:50], spline.knots = 4, spline.degree = 3) ## extracting the spline transformation settings spline.param <- attr(B1, "splineInterval") ## use the same settings to apply to the next 50 observations B2 <- isb(x[-(1:50)], spline.degree = 3, knots = spline.param)## plot the spline transformation given a monotone sequence B0 <- isb(0:100, spline.knots = 2, spline.degree = 3) plot(NULL, xlim = c(0, 140), ylim = c(0, 1), xlab = "x", ylab = "I-spline") for (i in 1:ncol(B0)) { lines(B0[, i], col = i, lwd = 3) } legend("bottomright", legend = 1:ncol(B0), col = 1:ncol(B0), lty = 1, lwd = 3, title = "Spline Columns" ) ## create I-spline basis for the first 50 observations x <- iris$Sepal.Length B1 <- isb(x[1:50], spline.knots = 4, spline.degree = 3) ## extracting the spline transformation settings spline.param <- attr(B1, "splineInterval") ## use the same settings to apply to the next 50 observations B2 <- isb(x[-(1:50)], spline.degree = 3, knots = spline.param)
Inner function call to create I-splines based on the
user defined knots and polynomial degree d of the splines
isplinebasis(x, knots, d)isplinebasis(x, knots, d)
x |
a scalar or vector of values which will be transformed into splines |
knots |
a vector of knot values of the splines |
d |
the polynomial degree of the splines |
a matrix with for each value of x the corresponding spline values.
Standardize the columns of an attribute matrix X to zscores, to the
range [0 1] or a prespecified scale.
normalize(x, standardize = "zscore")normalize(x, standardize = "zscore")
x |
An attribute variable which will be scaled. |
standardize |
Either a string value denoting a predefined scaling, or a
list with values |
The standardized matrix. The numeric centering and scalings used are
returned as attribute "standardize".
Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
## standardize the first 50 objects to zscores x <- iris$Sepal.Length x1 <- normalize(x[1:50], standardize = "zscore") ## use the same settings to apply to the next 100 observations x2 <- normalize(x[-(1:50)], standardize = attr(x1, "standardization"))## standardize the first 50 objects to zscores x <- iris$Sepal.Length x1 <- normalize(x[1:50], standardize = "zscore") ## use the same settings to apply to the next 100 observations x2 <- normalize(x[-(1:50)], standardize = attr(x1, "standardization"))
This function plots the hinge object created by getHinge.
## S3 method for class 'hinge' plot(x, y = 1, z = NULL, ...)## S3 method for class 'hinge' plot(x, y = 1, z = NULL, ...)
x |
The hinge object returned from |
y |
Specifies the class ( |
z |
If specified, the majorization function with the supporting point
|
... |
Other arguments passed to plot method. |
hingefunction <- getHinge() ## plot hinge function value plot(hingefunction, z = 3)hingefunction <- getHinge() ## plot hinge function value plot(hingefunction, z = 3)
Shows the results of the cross validation graphically.
Possible graphics are among others the distribution of
the predicted values q per class per lambda value
and the misclassification rate per lambda.
## S3 method for class 'svmmajcrossval' plot(x, type = "grid", ...)## S3 method for class 'svmmajcrossval' plot(x, type = "grid", ...)
x |
the |
type |
the type of graph being shown, possible values are
|
... |
Further arguments passed to or from other methods. |
Shows, one graph per attribute, the weights of all attributes. The type of graph depends on the type of the attribute: the spline line of the corresponding attribute in case a spline has been used, a bar plot for categorical and logical values, and a linear line for all other type of the attribute values. This function cannot be used in a model with a non-linear kernel.
plotWeights(object, plotdim = c(3, 3), ...)plotWeights(object, plotdim = c(3, 3), ...)
object |
The model returned from |
plotdim |
A vector of the form |
... |
other parameters given to the |
This function predicts the predicted value (including intercept), given a
previous trained model which has been returned by
svmmaj.
## S3 method for class 'svmmaj' predict(object, X.new, y = NULL, weights = NULL, show.plot = FALSE, ...)## S3 method for class 'svmmaj' predict(object, X.new, y = NULL, weights = NULL, show.plot = FALSE, ...)
object |
Model which has been trained beforehand using
|
X.new |
Attribute matrix of the objects to be predicted, which has the
same number of attributes as the untransformed attribute matrix in
|
y |
The actual class labels (only if |
weights |
The weight of observation as the relative importance of the prediction error of the observation. |
show.plot |
If |
... |
Arguments to be passed to methods. |
The predicted value (including intercept) of class q.svmmaj,
with attributes:
y |
The observed class labels of each object. |
yhat |
he predicted class labels of each object. |
classes |
The class labels. |
Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
attach(AusCredit) ## model training model <- svmmaj(X[1:400, ], y[1:400], hinge = "quadratic", lambda = 1) ## model prediction q4 <- predict(model, X[-(1:400), ], y[-(1:400)], show.plot = TRUE) q4attach(AusCredit) ## model training model <- svmmaj(X[1:400, ], y[1:400], hinge = "quadratic", lambda = 1) ## model prediction q4 <- predict(model, X[-(1:400), ], y[-(1:400)], show.plot = TRUE) q4
Given the input parameters, which are generated from
transformdata, it performs the same transformation
with the same settings to the given input
## S3 method for class 'transDat' predict( x, attrib = NULL, values = NULL, standardization = NULL, splineInterval = NULL, splineDegree = NULL )## S3 method for class 'transDat' predict( x, attrib = NULL, values = NULL, standardization = NULL, splineInterval = NULL, splineDegree = NULL )
x |
a (new) vector of numerics to be transformed |
attrib |
either a list of settings, or |
values |
a vector of levels in case |
standardization |
the standardization rules from |
splineInterval |
the knots to be used for spline basis |
splineDegree |
the polynomial degree of the splines |
a transformed data based on the user defined settings
SVM-Maj is an algorithm to compute a support vector machine (SVM) solution.
In its most simple form, it aims at finding hyperplane that optimally
separates two given classes. This objective is equivalent to finding a
linear combination of k predictor variables to predict the two
classes for n observations. SVM-Maj minimizes the standard support
vector machine (SVM) loss function. The algorithm uses three efficient
updates for three different situations: primal method which is efficient in
the case of n > k, the decomposition method, used when the matrix of
predictor variables is not of full rank, and a dual method, that is
efficient when n < k. Apart from the standard absolute hinge error,
SVM-Maj can also handle the quadratic and the Huber hinge.
## S3 method for class 'q.svmmaj' print(x, ...) svmmaj( X, y, lambda = 1, weights.obs = 1, weights.var = 1, scale = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1L, kernel = vanilladot, kernel.sigma = 1, kernel.scale = 1, kernel.degree = 1, kernel.offset = 1, hinge = c("absolute", "quadratic", "huber", "logitistic"), hinge.delta = 1e-08, options = setSVMoptions(), initial.point = NULL, verbose = FALSE, na.action = na.omit, ... ) ## Default S3 method: svmmaj( X, y, lambda = 1, weights.obs = 1, weights.var = 1, scale = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1L, kernel = vanilladot, kernel.sigma = 1, kernel.scale = 1, kernel.degree = 1, kernel.offset = 1, hinge = c("absolute", "quadratic", "huber", "logitistic"), hinge.delta = 1e-08, options = setSVMoptions(), initial.point = NULL, verbose = FALSE, na.action = na.omit, ... )## S3 method for class 'q.svmmaj' print(x, ...) svmmaj( X, y, lambda = 1, weights.obs = 1, weights.var = 1, scale = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1L, kernel = vanilladot, kernel.sigma = 1, kernel.scale = 1, kernel.degree = 1, kernel.offset = 1, hinge = c("absolute", "quadratic", "huber", "logitistic"), hinge.delta = 1e-08, options = setSVMoptions(), initial.point = NULL, verbose = FALSE, na.action = na.omit, ... ) ## Default S3 method: svmmaj( X, y, lambda = 1, weights.obs = 1, weights.var = 1, scale = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1L, kernel = vanilladot, kernel.sigma = 1, kernel.scale = 1, kernel.degree = 1, kernel.offset = 1, hinge = c("absolute", "quadratic", "huber", "logitistic"), hinge.delta = 1e-08, options = setSVMoptions(), initial.point = NULL, verbose = FALSE, na.action = na.omit, ... )
x |
the |
... |
Other arguments passed to methods. |
X |
A data frame (or object coercible by
|
y |
A factor (or object coercible by |
lambda |
Regularization parameter of the penalty term. |
weights.obs |
a vector of length |
weights.var |
a vector of length |
scale |
Specifies whether the columns of attribute matrix |
spline.knots |
equals the number of internal knots of the spline basis.
When the number of knots exceeds the number of (categorical) values of
an explanatory variable, the duplicate knots will be removed using
|
spline.degree |
equals the polynomial degree of the splines,
for no splines: |
kernel |
Specifies which kernel function to be used (see
|
kernel.sigma |
additional parameters used for the kernel function
(see |
kernel.scale |
additional parameters used for the kernel function
(see |
kernel.degree |
additional parameters used for the kernel function
(see |
kernel.offset |
additional parameters used for the kernel function
(see |
hinge |
Specifies with hinge function from
|
hinge.delta |
The parameter of the huber hinge
(only if |
options |
additional settings used in the |
initial.point |
Initial solution. |
verbose |
|
na.action |
Generic function for handling NA values. |
The following settings can be added as element in the options
parameter:
decomposition Specifies whether the QR decomposition should be used
for efficient updates. Possible values are 'svd' for Singular value
decomposition (Eigenvalue decomposition for non-linear kernel) or
'chol' for Cholesky (or QR decomposition in case of linear kernel)
convergence Specifies the convergence criterion of the algorithm.
Default is 1e-08.
increase.step The iteration number from which relaxed update will be
used.
eps The relaxation of the majorization function for absolute hinge:
.25 * eps^-1 is the maximum steepness of the majorization function.
check.positive Specifies whether a check has to be made for positive
input values.
max.iter maximum number of iterations to use
Returns a svmmaj-class object,
of which the methods plot,
plotWeights, summary and predict can be applied.
(see also predict.svmmaj and
print.svmmaj)
Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
dots for the computations of the kernels.
predict.svmmaj
normalize
isb
getHinge
## using default settings model1 <- svmmaj( diabetes$X, diabetes$y, hinge = "quadratic", lambda = 1 ) summary(model1) weights.obs <- list(positive = 2, negative = 1) ## using radial basis kernel library(kernlab) model2 <- svmmaj( diabetes$X, diabetes$y, hinge = "quadratic", lambda = 1, weights.obs = weights.obs, scale = "interval", kernel = rbfdot, kernel.sigma = 1 ) summary(model2) ## I-spline basis library(ggplot2) model3 <- svmmaj( diabetes$X, diabetes$y, weight.obs = weight.obs, spline.knots = 3, spline.degree = 2 ) plotWeights(model3, plotdim = c(2, 4))## using default settings model1 <- svmmaj( diabetes$X, diabetes$y, hinge = "quadratic", lambda = 1 ) summary(model1) weights.obs <- list(positive = 2, negative = 1) ## using radial basis kernel library(kernlab) model2 <- svmmaj( diabetes$X, diabetes$y, hinge = "quadratic", lambda = 1, weights.obs = weights.obs, scale = "interval", kernel = rbfdot, kernel.sigma = 1 ) summary(model2) ## I-spline basis library(ggplot2) model3 <- svmmaj( diabetes$X, diabetes$y, weight.obs = weight.obs, spline.knots = 3, spline.degree = 2 ) plotWeights(model3, plotdim = c(2, 4))
Trained SVM model as output from svmmaj.
The returning object consist of the following values:
The function specifications which has been called.
The regularization parameter of the penalty term which has been used.
The corresponding loss function value of the final solution.
Number of iterations needed to evaluate the algorithm.
The attribute matrix of dim(X) = c(n,k).
The vector of length n with the actual class labels.
These labels can be numeric [0 1] or two strings.
A vector of length n with the predicted
class labels of each object, derived from q.tilde
The attribute matrix X after standardization and
(if specified) spline transformation.
The applied normalization parameters
(see normalize).
The spline knots which has been used
(see isb).
Denotes the number of spline basis of
each explanatory variable in X.
The decomposition matrices used in estimating the model.
The hinge function which has been used
(see getHinge).
If identified, the beta parameters for the linear combination (only available for linear kernel).
A vector of length n with predicted values of
each object including the intercept.
Number of support vectors.
## S3 method for class 'svmmaj' print(x, ...) ## S3 method for class 'svmmaj' summary(object, ...) ## S3 method for class 'summary.svmmaj' print(x, ...) ## S3 method for class 'svmmaj' plot(x, ...)## S3 method for class 'svmmaj' print(x, ...) ## S3 method for class 'svmmaj' summary(object, ...) ## S3 method for class 'summary.svmmaj' print(x, ...) ## S3 method for class 'svmmaj' plot(x, ...)
x |
the |
... |
further arguments passed to or from other methods. |
object |
the |
Prints the result from the cross validation procedure in
svmmajcrossval.
## S3 method for class 'svmmajcrossval' print(x, ...) ## S3 method for class 'svmmajcrossval' summary(object, ...)## S3 method for class 'svmmajcrossval' print(x, ...) ## S3 method for class 'svmmajcrossval' summary(object, ...)
x |
the cross-validation output from |
... |
ignored |
object |
the output object from |
Given the predicted values q and its corresponding
observed classes y, it shows its separation performances
by showing the roc-curve.
roccurve(q, y = attr(q, "y"), class = 1, ...)roccurve(q, y = attr(q, "y"), class = 1, ...)
q |
the predicted values |
y |
a list of the actual classes of |
class |
the base class to show the roc-curve |
... |
additional parameters given as input to the |
model <- svmmaj(diabetes$X, diabetes$y) roccurve(model$q)model <- svmmaj(diabetes$X, diabetes$y) roccurve(model$q)
This
This dataframe contains the following columns
Identifier of the store
The city of the store
The zip code of the store
head(supermarket1996, 3)head(supermarket1996, 3)
This function performs a gridsearch of k-fold cross-validations using SVM-Maj and returns the combination of input values which has the best forecasting performance.
svmmajcrossval( X, y, search.grid = list(lambda = 2^seq(5, -5, length.out = 19)), ..., convergence = 1e-04, weights.obs = 1, check.positive = TRUE, mc.cores = getOption("mc.cores"), options = NULL, verbose = FALSE, ngroup = 5, groups = NULL, return.model = FALSE )svmmajcrossval( X, y, search.grid = list(lambda = 2^seq(5, -5, length.out = 19)), ..., convergence = 1e-04, weights.obs = 1, check.positive = TRUE, mc.cores = getOption("mc.cores"), options = NULL, verbose = FALSE, ngroup = 5, groups = NULL, return.model = FALSE )
X |
A data frame (or object coercible by
|
y |
A factor (or object coercible by |
search.grid |
A list with for each factor the range of values to search for. |
... |
Other arguments to be passed through |
convergence |
Specifies the convergence criterion for |
weights.obs |
Weights for the classes. |
check.positive |
Specifies whether a check should be performed for
positive |
mc.cores |
the number of cores to be used (for parallel computing) |
options |
additional settings used in the |
verbose |
|
ngroup |
The number of groups to be divided into. |
groups |
A predetermined group division for performing the cross validation. |
return.model |
|
loss.opt |
The minimum (weighted) missclassification rate found in out-of-sample training along the search grid. |
param.opt |
The level of the factors which gives the minimum loss term value. |
loss.grp |
A list of missclassification rates per hold-out sample |
groups |
A vector defining the cross-validation groups which has been used. |
qhat |
The estimated out-of-sample predicted values in the cross-validation. |
qhat.in |
The trained predicted values |
param.grid |
The matrix of all gridpoints which has been performed during the cross-validation, with its corresponding weighted out-of-sample missclassification rate. |
model |
The |
Hok San Yip, Patrick J.F. Groenen, Georgi Nalbantov
P.J.F. Groenen, G. Nalbantov and J.C. Bioch (2008) SVM-Maj: a majorization approach to linear support vector machines with different hinge errors.
Xt <- diabetes$X yt <- diabetes$y ## performing gridsearch with k-fold cross-validation results <- svmmajcrossval( Xt, yt, scale = "interval", mc.cores = 2, ngroup = 5, return.model = TRUE ) summary(results$model) results plot(results) plot(results, "profile")Xt <- diabetes$X yt <- diabetes$y ## performing gridsearch with k-fold cross-validation results <- svmmajcrossval( Xt, yt, scale = "interval", mc.cores = 2, ngroup = 5, return.model = TRUE ) summary(results$model) results plot(results) plot(results, "profile")
Performs subsequently a normalization of the input data and creating spline basis based on the user defined input
transformdata( x, standardize = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1 )transformdata( x, standardize = c("interval", "zscore", "none"), spline.knots = 0, spline.degree = 1 )
x |
a single column of values as input for the data transformation |
standardize |
Either a string value denoting a predefined scaling, or a
list with values |
spline.knots |
Number of inner knots to use. |
spline.degree |
The polynomial degree of the spline basis. |
transformed data in spline basis or (in case of no spline) a normalized vector
1984 United Stated Congressional Voting Records; Classify as Republican or Democrat.
X is a data frame with 434 congress members and 16 attributes: 16 key
votes identified by the Congressional Quarterly Almanac (CQA). All
attributes are binary values, with 1= yes and 0= no.
X1 |
handicapped-infants |
X2 |
water-project-cost-sharing |
X3 |
adoption-of-the-budget-resolution |
X4 |
physician-fee-freeze |
X5 |
el-salvador-aid |
X6 |
religious-groups-in-schools |
X7 |
anti-satellite-test-ban |
X8 |
aid-to-nicaraguan-contras |
X9 |
mx-missile |
X10 |
immigration |
X11 |
synfuels-corporation-cutback |
X12 |
education-spending |
X13 |
superfund-right-to-sue |
X14 |
crime |
X15 |
duty-free-exports |
X16 |
export-administration-act-south-africa |
y consists factors which denotes whether the congress member is a
Republican or a Democrat.
The training set voting.tr contains a randomly selected set of 300
subjects, and voting.te contains the remaining 134 subjects.
voting contains all 434 objects.
This data set includes votes for each of the U.S. House of Representatives Congressmen on the 16 key votes identified by the CQA. The CQA lists nine different types of votes: voted for, paired for, and announced for (these three simplified to yea), voted against, paired against, and announced against (these three simplified to nay), voted present, voted present to avoid conflict of interest, and did not vote or otherwise make a position known (these three simplified to an unknown disposition).
Chih-Chung Chang and Chih-Jen Lin, LIBSVM : a library for support vector machines, 2001. Software available at https://www.csie.ntu.edu.tw/~cjlin/libsvm/.
attach(voting) summary(X) summary(y)attach(voting) summary(X) summary(y)
For efficiency use in svmmajcrossval
X.svmmaj(object, X.new, weights = NULL)X.svmmaj(object, X.new, weights = NULL)
object |
Model which has been trained beforehand using
|
X.new |
Attribute matrix of the objects to be predicted, which has the
same number of attributes as the untransformed attribute matrix in
|
weights |
The weight of observation as the relative importance of the prediction error of the observation. |